Probability Theory in Statistical Physics, Percolation, and Other Random Topics: The Work of C. Newman

DOI10.1007/978-981-15-0294-1_1zbMath1446.82084arXiv2002.00342OpenAlexW2980469806MaRDI QIDQ3297355

Federico Camia, Daniel L. Stein

Publication date: 3 July 2020

Published in: Springer Proceedings in Mathematics & Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2002.00342

zbMATH Keywords

critical exponentspercolationspin glassesnormal fluctuationsRiemann hypothesispure statescontinuum scaling limitground statesSLEBrownian webfirst passage percolationFK percolationEdwards-Anderson modelreplica symmetry breakingLee-Yang theoremmetastaterandom cluster representationCLEIsing field theorydeep quenchFortuin-KasteleyndeBruijn-Newman constantnature vs. nurture

Mathematics Subject Classification ID

Brownian motion (60J65) Combinatorial probability (60C05) History of mathematics in the 21st century (01A61) Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses) (82D30) Symmetry breaking in quantum theory (81R40) Phase transitions (general) in equilibrium statistical mechanics (82B26) Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics (82C20) Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics (82B41) Percolation (82B43) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Critical phenomena in equilibrium statistical mechanics (82B27) Dynamics of random walks, random surfaces, lattice animals, etc. in time-dependent statistical mechanics (82C41) Dynamics of disordered systems (random Ising systems, etc.) in time-dependent statistical mechanics (82C44) Statistical mechanics of magnetic materials (82D40) History of statistical mechanics (82-03)

Cites Work

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• Conformal radii for conformal loop ensembles
• The scaling limit geometry of near-critical 2D percolation
• Two-dimensional scaling limits via marked nonsimple loops
• Excursion decompositions for SLE and Watts' crossing formula
• Two-dimensional critical percolation: the full scaling limit
• The conformal loop ensemble nesting field
• Mean-field critical behaviour for percolation in high dimensions
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• Exploration trees and conformal loop ensembles
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• Normal fluctuations and the FKG inequalities
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• Conformal loop ensembles: the Markovian characterization and the loop-soup construction
• Conformal loop ensembles and the stress-energy tensor
• The universal relation between scaling exponents in first-passage percolation
• Examples of nonpolygonal limit shapes in i.i.d. first-passage percolation and infinite coexistence in spatial growth models
• Differentiability at the edge of the percolation cone and related results in first-passage percolation
• The link overlap and finite size effects for the 3D Ising spin glass
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• Axioms for Euclidean Green's functions
• FK-Ising coupling applied to near-critical planar models
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• Planar Ising magnetization field. I: Uniqueness of the critical scaling limit
• Conformal invariance of spin correlations in the planar Ising model
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• Basic properties of SLE
• On the de Bruijn-Newman constant
• Lee-Yang property and Gaussian multiplicative chaos
• The Brownian net
• The percolation signature of the spin glass transition
• Superdiffusivity in first-passage percolation
• Competition interfaces and second class particles
• Random subgraphs of finite graphs. II: The lace expansion and the triangle condition
• Critical percolation exploration path and \(\mathrm{SLE}_{6}\): a proof of convergence
• The roots of trigonometric integrals
• Replica symmetry breaking and the nature of the spin glass phase
• Phase transitions on nonamenable graphs
• Critical percolation in the plane: conformal invariance, Cardy's formula, scaling limits
• A shape theorem and semi-infinite geodesics for the Hammersley model with random weights
• Moderate deviations for the chemical distance in Bernoulli percolation
• Some applications of the Lee-Yang theorem
• Calculus on manifolds of conformal maps and CFT
• The Importance of the Ising Model
• CONFORMAL INVARIANCE OF ISING MODEL CORRELATIONS
• Ising (conformal) fields and cluster area measures
• An improved lower bound for the de Bruijn-Newman constant
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• Pivotal, cluster, and interface measures for critical planar percolation
• The Brownian Web
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